Genghis,
Unfortunately, your experience is not atypical at Coventry. I've known cases of people being held for over half and hour at A1 and C2. I once went on a short, half-hour training flight only to return and orbit for ten minutes whilst the aircraft which had started up at the same time as me was still waiting for an airways clearance to be relayed from Birmingham on the runway.
Part of the trouble is the interminable runway closures which have been going on since last Autumn, including taxiway closures which create terrible bottlenecks. As a result, the commercial traffic does seem to get priority. Fortunately, my training has finished at Coventry, but it was a bit of a headache.
Generally the service at Coventry is good. During the summer, when hour-building, I visited several times and had no complaints. It is the WIP which has created a number of problems which each have a knock on effect. The only answer is to plan for it, but it's not necessarily easy to know as the WIP plans seem to change at short notice.